Electromagnetic field and frequency

[sweet springs]

Electromagnetism gives the energy density $\frac{\epsilon_0}{2}E^2+\frac{1}{2\mu_0}B^2$. It does not include frequency $\nu$ or $\omega$ at least explicitly that QM or photon needs. For an example static electric field has nothing to do with frequency but has energy. How should I incorporate these two views?

 

[DrClaude]

How should I incorporate these two views?

Don't!

There is no need to introduce photons here, and it will only detract you from understanding what is going on. Threat the electric and magnetic fields as fields, and electromagnetic waves as waves, and everything will work out.

If you absolutely need to reconcile it with a photon concept, you would simply have more or fewer photons for the same energy density, depending on the frequency of the photons.

 

[sweet springs]

Thanks for your advice. I will follow.

 

[vanhees71]

Don't!

There is no need to introduce photons here, and it will only detract you from understanding what is going on. Threat the electric and magnetic fields as fields, and electromagnetic waves as waves, and everything will work out.

If you absolutely need to reconcile it with a photon concept, you would simply have more or fewer photons for the same energy density, depending on the frequency of the photons.

To add to the above list of advices: Also treat photons as (quantum) fields. They are in no way similar to anything you'd call a particle in everyday life, and in the 21st century relativstic QT should be learned only as QFT. A first-quantization approach is outdated and misleading!